double sink vanity rough plumbing -- please check my plan

I am a DIY working on a bathroom remodel which includes converting a single sink vanity into a double. I have done enough plumbing in the past to feel reasonably confident, and have read extensively here; I want to make sure I understand what is needed.

Here is the current plumbing:

Also a close-up -- anybody see a problem with what the original builder did here?!? (How exactly do you drive a drywall screw through a stud plate and not know it??)

The new vanity will position the right-hand sink just about where the current stack is. The left hand sink will be about 16" to the left of where the original sink was -- i.e., it will need to move left one stud bay.

After a good bit of thought, here is what I am planning, assuming that I get a green light from the knowledgeable folks on this forum:

Cut the current 2" ABS stack above and below the current tee junction. Change over to PVC using flexible couplings (unless you think I should join with the green cement -- ??) -- changing to PVC because it is easier for me to source, and cheaper even counting in the cost of the couplings. Put a double fixture tee (2" x 2" x 1.5" x 1.5") in where the current sanitary tee is. On the right, the double fixture tee will immediately join with a 1.5" elbow to bring the right-hand sink drain out of the wall. On the left will be about a 32" run of 1.5" drain, then an elbow to bring the left-hand sink drain out of the wall.

Questions:

1) Am I right in thinking the horizontal runs need to drain a minimum of 1/4" per foot?

2) Is it a problem to go right from the double tee to the elbow out of the wall?

3) Is it a problem that the left and right sides of this will be so different in length?

4) All I can find at the local hardware stores (both big box and small town) are double sanitary tees, but my understanding is that that is not optimal, even if it were to pass code. So I have found double fixture tees on-line, - or at least, I think I have. It seems that these are called a hundred different things. I want to be sure that either or both of these are in fact the right fixture:

What I'm seeing is a picture of an ABS fitting, rather than the PVC fittings I tried to link to. The one that I am reasonably sure is correct is for a Spears P500-251 PVC Double-Fixture Wye. I need to have 2" top and bottom, and 1.5" on either side -- the vent is 2" going up. And no, I can't find a local store that carries any such thing ... but I live out in the boonies, so that may have something to do with it.

If you feel compelled to advertise for online companies, please send me a check first.
You can ask and answer questiosn without advertising.
Just stick to the plumbing questions, and don't feel you need to send people to your favorite retailer.
What do you do for a living? I would love to advertise your competitor for free here. Maybe we can put a dent in your business. I can make it an ad on every page. Buy from Awake's competitor!

And by the way, ABS goes with ABS and PVC goes with PVC.
If you switch to PVC with couplings, it will need to be the shielded couplings to prevent the pipes from shifting. You can't use the rubber Ferncos.

My apologies -- it was not my intention at all to advertise for a particular retailer. I seem to have poked a sore spot, and I certainly did not mean to. I just wanted to be sure that I had found the correct fitting; that was my only intention in posting the link. I hadn't understood what had happened to the links, but now I realize that they were violating the rules of the forum. Again, please accept my apologies.

Yes, I know that ABS goes with ABS, and PVC goes with PVC ... but I thought -- apparently incorrectly -- that I had read here that the rubber fittings were the proper way to deal with the transition. I have not heard of the shielded couplings; any chance you could post or send me a link (presumably, to an acceptable retailer! )?

These are two brands. And there are more.
Most stores will carry something like them. HD and Lowes for sure.
The metal wrap keeps the pipes aligned.
All of us plumbers have seen rubber fittings that have sagged badly over time. Our plumbing inspectors don't let us use them.

Again, many thanks. I am seeing something in the first picture that makes me wonder if these are intended to be used only with specific types of material -- e.g., this one only joins CI to PVC, while that one only joins ABS to PVC -- or do they work with any combination of materials?

I am NOT trying to cause any problems with my next question, but only to make sure I learn the rules of the forum: based on your last post, is it okay to mention big-box stores by name? Part of my confusion also is having seen a link in an old post to a different on-line retailer, so I am genuinely not sure what is allowed and what isn't. Again, I am not trying to cause any problems -- on the contrary, I want to be sure I don't cause problems in the future!

Jeff Bezos from Amazon went on 60 minutes last December.
Asked about his plan for the future, he said he would run at a loss for eight years, and after that all the competion would be out of business. And then he started laughing.
Jeff is worth 26 billion now. Not enough though.
When Amazon found out I was selling high end plumbing, they took over the market.
They then called me and wanted my labor too. So first they took over my product sales as best they could, and then they wanted my labor sales. There is no way any business in plumbing could stay alive getting half their labor and none of their product sales.
I would still be required to be a State Licensed Plumber, carry bonding and insurance, pay for employees, work vans, phones and an office. I have to follow the rules for being a Washington State contractor. Amazon doesn't have to as far as I know. They expect the little guys to do all that.
Amazon would hold the money, and if they decided I wasn't Amazon enough for them, could legally withhold money forever. Which they have done to other business owners.
They now are asking auto shops that do oil changes, to give up their parts and accept half the labor for being on Amazon. Since a good company makes a 5% profit, you can imaging how quickly anyone that does business that way will fail.
Thursday I go out to Vashon Island and install a TOTO Drake II with Sanagloss and a TOTO S300e Washlet with installation. But it's my customer.
If you check out this link, there was a customer in the San Juan's that after three deliveries, still didn't have a complete toilet. He kept getting broken porcelain in bent boxes.

Terry, that helps to provide the context. I certainly understand your anger with them. For a DIY like me, it becomes a real dilemma -- the big outfits have driven the smaller stores and independent suppliers out of business, especially in an out-of-the-way place like where I live, leaving me with few options for finding supplies. Round and round it goes ...

I am a bookoholic in rural Montana so online is wonderful, except that they are doing the same sort of thing that Terry talked about with authors and publishers, even refusing to sell their product if they don't go along with the gag. I have decided to quit buying from them.

These are two brands. And there are more.
Most stores will carry something like them. HD and Lowes for sure.
The metal wrap keeps the pipes aligned.
All of us plumbers have seen rubber fittings that have sagged badly over time. Our plumbing inspectors don't let us use them.

These are two brands. And there are more.
Most stores will carry something like them. HD and Lowes for sure.
The metal wrap keeps the pipes aligned.
All of us plumbers have seen rubber fittings that have sagged badly over time. Our plumbing inspectors don't let us use them.